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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク camera matrix ： ウィキペディア英語版 camera matrix In computer vision a camera matrix or (camera) projection matrix is a $3\; \backslash times\; 4$ matrix which describes the mapping of a pinhole camera from 3D points in the world to 2D points in an image. Let $\backslash mathbf$ be a representation of a 3D point in homogeneous coordinates (a 4-dimensional vector), and let $\backslash mathbf$ be a representation of the image of this point in the pinhole camera (a 3-dimensional vector). Then the following relation holds : $\backslash mathbf\; \backslash sim\; \backslash mathbf\; \backslash ,\; \backslash mathbf$ where $\backslash mathbf$ is the camera matrix and the $\backslash ,\; \backslash sim$ sign implies that the left and right hand sides are equal up to a non-zero scalar multiplication. Since the camera matrix $\backslash mathbf$ is involved in the mapping between elements of two projective spaces, it too can be regarded as a projective element. This means that it has only 11 degrees of freedom since any multiplication by a non-zero scalar results in an equivalent camera matrix. == Derivation == The mapping from the coordinates of a 3D point P to the 2D image coordinates of the point's projection onto the image plane, according to the pinhole camera model is given by : $\backslash begin\; y\_1\; \backslash \backslash \; y\_2\; \backslash end\; =\; \backslash frac\; \backslash begin\; x\_1\; \backslash \backslash \; x\_2\; \backslash end$ where $(x\_1,\; x\_2,\; x\_3)$ are the 3D coordinates of P relative to a camera centered coordinate system, $(y\_1,\; y\_2)$ are the resulting image coordinates, and ''f'' is the camera's focal length for which we assume ''f'' > 0. Furthermore, we also assume that ''x3 > 0''. To derive the camera matrix this expression is rewritten in terms of homogeneous coordinates. Instead of the 2D vector $(y\_1,y\_2)$ we consider the projective element (a 3D vector) $\backslash mathbf\; =\; (y\_1,y\_2,1)$ and instead of equality we consider equality up to scaling by a non-zero number, denoted $\backslash ,\; \backslash sim$. First, we write the homogeneous image coordinates as expressions in the usual 3D coordinates. : $\backslash begin\; y\_1\; \backslash \backslash \; y\_2\; \backslash \backslash \; 1\; \backslash end\; =\; \backslash frac\; \backslash begin\; x\_1\; \backslash \backslash \; x\_2\; \backslash \backslash \; \backslash frac\; \backslash end\; \backslash sim\; \backslash begin\; x\_1\; \backslash \backslash \; x\_2\; \backslash \backslash \; \backslash frac\; \backslash end$ Finally, also the 3D coordinates are expressed in a homogeneous representation $\backslash mathbf$ and this is how the camera matrix appears: :   or   $\backslash mathbf\; \backslash sim\; \backslash mathbf\; \backslash ,\; \backslash mathbf$ where $\backslash mathbf$ is the camera matrix, which here is given by : , and the corresponding camera matrix now becomes : The last step is a consequence of $\backslash mathbf$ itself being a projective element. The camera matrix derived here may appear trivial in the sense that it contains very few non-zero elements. This depends to a large extent on the particular coordinate systems which have been chosen for the 3D and 2D points. In practice, however, other forms of camera matrices are common, as will be shown below. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「camera matrix」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.